Answer:
7.05 Hz
Explanation:
The natural frequency of a mass-spring system is:
[tex]f = \frac{1}{2 \pi}\sqrt{\frac{k}{m}}[/tex]
To determine the constant k of the spring we use Hooke's law:
Δl = F / k
k = F / Δl
In the first case the force was the weight of the 20 kg mass and the Δl was 20 mm.
F = m * a
F = 2 * 9.81 = 19.6 N
Then:
k = 19.6 / 0.02 = 980 N/m
Therefore:[tex]f = \frac{1}{2 \pi}\sqrt{\frac{980}{0.5}} = 7.05 Hz[/tex]
